A new fully decoupled strategy for reliability optimization based on adaptive Kriging with improved efficient global optimization and weighted K-means clustering

Abstract

Reliability-based design optimization (RBDO) is regarded as a more systematic approach to structural design that seamlessly combines reliability and design for optimization. However, the computational cost will be often substantial due to necessarily demanding reliability analysis during the optimization design procedure. This paper proposes a novel decoupling approach to effectively solve the RBDO problem. Based on the augmented reliability theory and Bayes’ rule, the failure probability function (FPF) is estimated through establishing a new adaptive Kriging model with an improved efficient global optimization (IEGO) and weighted K-means clustering (WKC). The WKC algorithm can effectively mitigate the clustering effect of the added sample points by partitioning original sample set into K clusters. Combined with IEGO, the sample points will be selected within each cluster that contribute the most to improving the Kriging model. This approach ensures the efficiency and accuracy of the adaptive Kriging model in estimating the FPF. The RBDO problem in which the probabilistic constraints are substituted using the estimated FPF can be fully decoupled into a deterministic optimization problem, and demonstrated as an enabling efficient solution. Thus, it is worth noting that the primary computational cost associated with the decoupling process arises from estimating the FPF. In this paper, the computational cost of solving the RBDO is significantly reduced by developing an adaptive Kriging model capable of estimating the FPF accurately and efficiently. One numerical example and three practical engineering applications are employed to demonstrate the accuracy and efficiency of the proposed method compared to other methods.